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math.AP2023
Hölder and Sobolev regularity of optimal transportation potentials with rough measures
Pierre-Emmanuel Jabin, Antoine Mellet
We consider a Kantorovich potential associated to an optimal transportation problem between measures that are not necessarily absolutely continuous with respect to the Lebesgue mea…
math.AP2023
Hele-Shaw flow as a singular limit of a Keller-Segel system with nonlinear diffusion
Antoine Mellet
We study a singular limit of the classical parabolic-elliptic Patlak-Keller-Segel (PKS) model for chemotaxis with non linear diffusion. The main result is the convergence of th…